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Applied Thermal Engineering xxx (2011) 1e12

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Applied Thermal Engineering

journal homepage: www.elsevier .com/locate/apthermeng

Thermodynamic and exergoenvironmental analyses, and multi-objectiveoptimization of a gas turbine power plant

Pouria Ahmadi*, Ibrahim DincerDepartment of Mechanical Engineering, Faculty of Engineering and Applied Science, University of Ontario Institute of Technology (UOIT), 2000 Simcoe St. North, Oshawa,ON L1H 7K4, Canada

a r t i c l e i n f o

Article history:Received 13 November 2010Accepted 12 April 2011Available online xxx

Keywords:EnergyExergyEfficiencyOptimizationExergoeconomicsGenetic algorithmSustainabilityEnvironmental impact

* Corresponding author.E-mail addresses: pouryaahmadi81@gmail.co

(P. Ahmadi).

1359-4311/$ e see front matter � 2011 Elsevier Ltd.doi:10.1016/j.applthermaleng.2011.04.018

Please cite this article in press as: P. Ahmadi,a gas turbine power plant, Applied Thermal

a b s t r a c t

The present study deals with a comprehensive thermodynamic and exergoeconomic modeling of a GasTurbine (GT) power plant. In order to validate the thermodynamic model, the results are compared withone of the largest gas turbine power plants in Iran (known as Shahid Salimi Gas Turbine power plant).Moreover, a multi-objective optimization is performed to find the best design variables. The designparameters considered here are air compressor pressure ratio (rAC), compressor isentropic efficiency(hAC), gas turbine isentropic efficiency (hGT), combustion chamber inlet temperature (T3) and gas turbineinlet temperature (TIT). In the multi-objective optimization approach, certain exergetic, economic andenvironmental parameters are considered through two objective functions, including the gas turbineexergy efficiency, total cost rate of the system production including cost rate of environmental impact. Inaddition, fast and effective non-dominated sorting genetic algorithm (NSGA-II) is applied for the opti-mization purpose. The thermoenviroeconomic objective function is minimized while power plant exergyefficiency is maximized using a power full developed genetic algorithm. The results of optimal designsare obtained as a set of multiple optimum solutions, called ‘the Pareto optimal solutions’. Moreover, theoptimized results are compared with the working data from the case study. These show that by selectingthe optimized data 50.50% reduction in environmental impacts is obtained. Finally, sensitivity analysis ofchange in objective functions, when the optimum design parameters vary, is performed and the degreeof each parameter on conflicting objective functions has been determined.

� 2011 Elsevier Ltd. All rights reserved.

1. Introduction

Energy is a key driver for almost everything and is essential inour daily life and activities in various sectors, ranging from resi-dential to industrial application. Due to the increasing fuel pricesand decreasing fossil fuel resources, the optimum management ofenergy resources and applications is of great importance.

Gas Turbine (GT) power plants are widely utilized throughoutthe world for electricity generation, and natural gas is often usedas a common fuel in such plants. Today, many electrical gener-ating utilities are striving to improve the efficiency (or heat rate)at their existing thermal electric generating stations; many ofthem are over 25 years old. Often, a heat rate improvement ofonly a few percent appears desirable since it is thought that thecosts and complexity of such measures may be more manageable

m, pouria.ahmadi@uoit.ca

All rights reserved.

I. Dincer, Thermodynamic anEngineering (2011), doi:10.1

than more expensive options. In this regard, exergy based opti-mization is considered as one of the best tools for performanceassessment of power plants [1]. Energy utilization is very muchgoverned by thermodynamic principles (particularly by exergy)and, therefore, an understanding of exergetic aspects can help usunderstand pathways to sustainable development [2,3]. GTs areknown for their low-capital cost to power ratio, high flexibility,high reliability without complexity, short delivery time, earlycommissioning and commercial operation and very short startup and running times. Moreover, the combined cycle (CC) usesthe exhaust heat from the gas turbine engine to increase thepower plant output and boost the overall efficiency to beyond50% [1,2].

Recently, exergy analysis has been used by many researchers inthermal systems, especially for power plants. It is well-known thatthe exergy can be used to determine the location, type and truemagnitude of exergy destructions and losses. Therefore, it can playan important role in developing strategies and providing guidelinesfor more effective use of energy in the existing power plants. Somekey points about exergy are well explained in the literature [1,2,3]:

d exergoenvironmental analyses, and multi-objective optimization of016/j.applthermaleng.2011.04.018

P. Ahmadi, I. Dincer / Applied Thermal Engineering xxx (2011) 1e122

� Exergy has become increasingly important across a diversearray of fields and throughout developing and developedworldin order to increase efficiency, reduce wastes and losses, andimprove processes and systems.

� Exergy has become more integrated with economics andapplications as a new discipline like thermoeconomics orexergoeconomics.

� Exergy has been a tool to foster sustainability and contribute tomaking development more sustainable.

� Exergy has become more broadly covered in educationalprograms, and used as a basis for explaining and giving prac-tical meaning to the second-law of thermodynamics.

These remarks clearly show the importance of exergy in thermalengineering, especially for power plants. On the other hand, ther-moeconomics combines the exergy analysis with the economicprinciples and incorporates the associated costs of the thermody-namic inefficiencies in the total product cost of an energy system.These costs may help designers to understand the cost formationprocess in an energy system and it can be utilized in optimization ofthermodynamic systems, in which the task is usually focused onminimizing the unit cost of the system product [4,5]. Severalresearchers have carried out analyses with exergy and exer-goeconomics for gas turbine based integrated systems.

Sahin and Ali [6] carried out an optimal performance analysis ofa combined Carnot cycle in a cascade form, including internalirreversibilities for steady-state operation. They obtained themaximum power and efficiency analytically and demonstrated theeffects of irreversibility parameters on maximum power output.Although exergy and exergoeconomic analysis are so importantand indispensable in power generation, they cannot find theoptimal design parameters in such systems. Therefore, using anoptimization procedure with respect to thermodynamics laws aswell as thermoeconomics is essential.

Ahmadi et al. [7] performed the multi-objective exergy basedoptimization of a CHP system for both heating and coolingproduction. They also carried out the sensitivity analysis to see thevariation of each design parameter on the system performancethrough energy and exergy analysis. In fact, the objectives in thisregard involved in the design optimization process were as follows[8]: thermodynamic (e.g., maximum efficiency, minimum fuelconsumption, minimum irreversibility and so on), economic (e.g.,minimum cost per unit of time, maximum profit per unit ofproduction) and environmental (e.g., limited emissions, minimumenvironmental impact). Some researchers have carried out theoptimization in power plant and CHP systems. They usually useevolutionary algorithm in their studies. Sahoo [9] carried out theexergoeconomic analysis and optimization of a cogenerationsystem using evolutionary programming. He considered a cogene-ration system which produced 50 MW of electricity and 15 kg/s ofsaturated steam at 2.5 bar. He optimized the unit using exer-goeconomic principles and evolutionary programming. The resultsshowed that for the optimum case in the exergoeconomic analysisthe cost of electricity and production cost are 9.9% lower incomparison with the base case. Ahmadi and Dincer [10] performedthe exergoeconomic optimization of a dual pressure combinedcycle power plant with supplementary firing. They considered thecost of exergy destruction in their objective function and optimizedit using a genetic algorithm.

Since environmental impact is one of the challenging problemsin this century, studying this kind of problem is of greatestimportance in all engineering fields. Therefore, some studies havebeen undertaken by considering this challenging problem. Dincer[11] considered the environmental and sustainability aspects ofhydrogen and fuel cell systems. He also analyzed the exergetic and

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environmental aspects of drying systems [12]. In addition to theexergetic and monetary costs of mass and energy streams in thethermal systems, environomic considers the costs related to flowsof pollutants [8,13]. However, by applying the unit damage costrelated to NOx and CO emissions [13], this objective function isformulated in the cost terms and it can be considered as anadditional economic objective. In this sense, the non-abbreviatedterm thermoenviroeconomic would be more appropriate, asrecognized by Frangopoulos [14]. Mozafari et al. [15] performedthe optimization of micro gas turbine by exergy, economic andenvironmental analysis. They performed their analysis for variousfuels. The optimization results showed that objective functionswere minimally affected by the type of fuel considered and thetrends of variations of second law efficiency and cost rate ofowning and operating the whole system are independent ofthe fuels.

Suresh et al. [16] performed the 3E (Energy, Exergy and Envi-ronment) analysis of advanced power plants based on high-ashcoal. Although they considered the environmental impact, theydid not optimize the cycle. In their study, the environmental impactof the power plants is estimated in terms of specific emissions ofCO2, SOx, NOx, and particulates. They concluded that the maximumpossible plant energy efficiency under the Indian climatic condi-tions using high ash Indian coal is about 42.3%.

In the present study, the thermodynamic modeling, second-law based thermodynamic analysis and multi-objective optimi-zation of a gas turbine power plant are conducted. Two completeobjective functions including the gas turbine exergy efficiency,total cost rate of the system product and the cost rate of envi-ronmental impact are considered. Further, the environmentalimpact is integrated with the thermoeconomic objective functionand defined as a new objective function in this study. The presentthermoenvironomic objective function is minimized while powerplant exergy efficiency is maximized using a genetic algorithm.Moreover, the sensitivity analysis of the changes in both objectivefunctions with variations of design parameters is carried out indetails. In this regard, the design parameters are compressorpressure ratio (rAC), compressor isentropic efficiency (hAC), gasturbine isentropic efficiency (hGT), combustion chamber inlettemperature (T3) and gas turbine inlet temperature (TIT). More-over, the sensitivity analysis is done in order to provide a goodinsight into this study. In this regard, the specific objectives of thispaper are as follows:

� To model a gas turbine power plant and compare the simula-tion code with an actual gas turbine power plant in Iran toensure the correctness of a simulation code.

� To introduce an objective function including exergy efficiency,total cost rate of the plant (including fuel cost, purchase cost,cost of exergy destruction and the cost rate of environmentalimpact)

� To use a modified version of evolutionary algorithm (i.e.,Genetic Algorithm (GA)) to use for multi objective optimizationpurpose.

� To define a new closed form equation for the exergy efficiencyin terms of total cost rate at the optimal design point.

� To perform sensitivity analysis of the design parameters onobjective functions to find the degree of dependency of eachparameter on objective functions conflicting.

2. Thermodynamic modeling

To find the optimum physical and thermal design parameters ofthe system, a simulation program is developed in Matlab software.

d exergoenvironmental analyses, and multi-objective optimization of016/j.applthermaleng.2011.04.018

P. Ahmadi, I. Dincer / Applied Thermal Engineering xxx (2011) 1e12 3

The temperature profile in gas turbine power plant, input andoutput enthalpy and exergy of each line in the plant are estimatedto study the multi objective optimization of the plant. The energybalance equations for various parts of the gas turbine plant that areshown in Fig. 1 are as follows:

� Air compressor

T2 ¼ T1 ��1þ 1

hAC

�rAC

ga�1ga

� 1��

(1)

_WAC ¼ _maCpaðT2 � T1Þ (2)

The Cpa in our analysis is considered a temperature variablefunction as follows [17]:

CPaðTÞ ¼ 1:04841��3:8371T

104

�þ 9:4537T2

107

!

� 5:49031T3

1010

!þ 7:9298T4

1014

!(3)

� Air Preheater

_maðh3 � h2Þ ¼ _mgðh5 � h6ÞhAP (4)

P3P2

¼ ð1� DPCCÞ (5)

� Combustion Chamber (CC)

_mah3 þ _mf LHV ¼ _mgh4 þ ð1� hccÞ _mf LHV (6)

P4P3

¼ ð1� DPccÞ (7)

The combustion equation is:

Fig. 1. Schematic diagram of th

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lCx1Hy1 þ�xO2

O2 þ xN2N2 þ xH2OH2Oþ xCO2

CO2 þ xArAr�/yCO2

CO2 þ yN2N2 þ yO2

O2 þ yH2OH2Oþ yNONOþ yCOCOþ yArAr

yCO2¼ �

l� x1 þ xCO2� yCO

�yN2

¼ xN2� yNO

yH2O ¼ xH2O þ l� y12

yO2¼ xO2

� l� x1 �l� y1

4� yCO

2� yNO

2yAr ¼ xAr

(8)

l ¼ nfuelnair

� Gas Turbine

T5 ¼ T4

8>><>>:1� hGT

26641�

�p4p5

�1� gggg

37759>>=>>; (9)

_WGT ¼ _mg$Cp;gðT5 � T6Þ (10)

_WNet ¼ _WGT � _WAC (11)

_mg ¼ _mf þ _ma (12)

where the Cpg is again considered a temperature variable functionas follows [17]:

CPgðTÞ ¼ 0:991615þ�6:99703T

105

�

þ 2:7129T2

107

!� 1:22442T3

1010

!(13)

These combinations of energy and mass balance equations werenumerically solved and the temperature and enthalpy of each lineof the plant were calculated.

e gas turbine power plant.

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Table 1The exergy destruction rate and exergy efficiency equations for plant components.

Components Exergy Destruction rate Exergy Efficiency

Compressor _ED;AC ¼ _E1 � _E2 � _EW ;AC hex;AC ¼_E2 � _E1_WAC

Combustion Chamber (CC) _ED;CC ¼ _E3 þ _E9 � _E4 hex;CC ¼_E4

_E3 þ _E9

Gas Turbine (GT) _ED;GT ¼ _EC � _ED � _WGT hex;GT ¼_WGT

_EC � _ED

Air Preheater (AP) _ED;AP ¼ Pi;AP

_E � Pe;AP

_E hex;AP ¼ 1�_ED;APPi;AP

_E

Table 2Operating conditions of the Shahid Salimi Gas Turbine Power Plant.

Name Unit Value

Natural gas mass flow rate to CC kg/s 8.44Air mass flow rate kg/s 491.55Lower heating value of natural gas kJ/kg 50916.96Compressor isentropic efficiency % 0.82Gas turbine isentropic efficiency % 0.86Air preheater effectiveness % 0.82Compressor pressure ratio e 10.1Gas turbine pressure ratio e 9.49Output power MW 132

P. Ahmadi, I. Dincer / Applied Thermal Engineering xxx (2011) 1e124

It should be noted, the thermodynamic model is developedbased on the following basic assumptions [4,17e19]:

� All the processes are considered steady state.� The principle of ideal-gas mixture is applied for the air andcombustion products.

� The fuel injected to the combustion chamber (CC) is assumed tobe a natural gas.

� Heat loss from the combustion chamber (CC) is considered tobe 3% of the fuel lower heating value (LHV). Moreover, all othercomponents are considered adiabatic.

� The dead state condition is P0 ¼ 1.01 bar and T0 ¼ 293.15 K.� In the preheater, 3% pressure drop is considered. Also, 3%pressure drop is considered in the combustion chamber (CC).

3. Exergy analysis

Exergy can be divided into four distinct components. The twoimportant ones are the physical exergy and chemical exergy. In thisstudy, the two other components which are kinetic exergy andpotential exergy are assumed to be negligible, as the changes inthem are negligible [1,2,20e25]. The physical exergy is defined asthe maximum theoretical useful work obtained as a system inter-acts with an equilibrium state [1]. The chemical exergy is associatedwith the departure of the chemical composition of a system from itschemical equilibrium. The chemical exergy is an important part ofexergy in combustion processes. Applying the first and the secondlaws of thermodynamics, the following exergy balance is obtained:

_ExQ þXi

_miexi ¼Xe

_meexe þ _ExW þ _ExD (14)

where subscripts e and i represent inlet and outlet specific exergy ofcontrol volume, respectively and _ExD, is the exergy destruction. Theother terms become

_ExQ ¼�1� T+

Ti

�_Qi and _ExW ¼ _W (15)

ex ¼ exph þ exch (16)

_ExQ and _ExW are the corresponding exergy of heat transfer andwork which cross the boundaries of the control volume, T is theabsolute temperature (K) and (+) refers to the ambient conditionsrespectively. In Eq. (14), term Ex is defined as follows:

_Ex ¼ _Exph þ _Exch (17)

where _Ex ¼ _mex:

The mixture chemical exergy is defined as follows [1,21,23]:

exchmix ¼"Xni¼1

Xiexchi þ RT0

Xni¼1

XiLnXi

#(18)

For the evaluation of the fuel exergy, the following exergy ratiois used:

x ¼ exf =LHVf (19)

For most of usual gaseous fuels, the ratio of chemical exergy tolower heating value is usually close to 1. Since the main fuel used inpower plants is methane, one may write xCH4

¼ 1:06 [1,21]:In this paper for the exergy analysis of the plant, the exergy of

each line is calculated at all states and the changes in the exergy are

Please cite this article in press as: P. Ahmadi, I. Dincer, Thermodynamic ana gas turbine power plant, Applied Thermal Engineering (2011), doi:10.1

determined for each major component. The source of exergydestruction (or irreversibility) in combustion chamber (CC) ismainly combustion or chemical reaction and thermal losses in theflow path respectively [1,23]. However, the exergy destruction inthe heat exchanger of the system i.e. air preheater is due to thelarge temperature difference between the hot and cold fluids. Theexergy destruction rate and the exergy efficiency for each compo-nent in the cycle (Fig. 1) are shown in Table 1. The operatingconditions for base case of the gas turbine power plant such as fuelmass flow rate and calorific value, output electrical power andefficiencies of compressor and GT are listed in Table 2.

4. Exergoeconomic analysis

4.1. Economic model

Finite natural resources andworld increasing energy demand bydeveloping countries are becoming increasingly important torecognize the mechanisms that degrade energy and resources andto develop systematic approaches for improving the design ofenergy systems and reducing the impact on the environment. Thesecond law of thermodynamics combined with economics repre-sents a very powerful tool for the systematic study and optimiza-tion of energy systems. This combination forms the basis of therelatively new field of thermoeconomics (exergoeconomics).Moreover, the economic model takes into account the cost of thecomponents including the amortization and maintenance and thecost of fuel combustion. In order to define a cost function whichdepends on optimization parameters of interest, component costshould be expressed as a function of thermodynamic designparameters [22]. The first study in this regard was proposed in thepaper called CGAM problem [26e28] which considered the ther-moeconomic analysis of a cogeneration plant to produce 14 kg/swater at 20 bar. Cost balance equations applied to the kth systemcomponents shows that the sum of cost rates associated with allexisting exergy stream equals the sum of cost rates of all enteringexergy streams plus the appropriate charges due to capitalinvestment and operating and maintenance expenses. The sum of

d exergoenvironmental analyses, and multi-objective optimization of016/j.applthermaleng.2011.04.018

P. Ahmadi, I. Dincer / Applied Thermal Engineering xxx (2011) 1e12 5

the last two terms is denoted by _Zk. For each flow line in the system,a parameter called flow cost rate C ($/s) was defined and the costbalance equation of each component can bewritten as follows [22]:Xe

_Ce;k þ _Cw;k ¼ _Cq;k þXi

_Ci;k þ _Zk (20)

The cost balances are generally written so that all terms arepositive. Using Eq. (20), one can write [1,20,22]:X�

ce _Ee�kþcw;k

_Wk ¼ cq;k _Eq;k þX�

ci _Ei�kþ _Zk (21)

_Cj ¼ cjEj (22)

The cost balance equations for all components of the systemconstructs a set of nonlinear algebraic equations, which was solvedfor Cj and cj.

In this analysis it is worth mentioning that the fuel and productexergy should be defined. The exergy product is defined accordingto the components under consideration. The fuel represents thesource that is consumed in generating the product. Both theproduct and fuel are expressed in terms of exergy. The cost ratesassociated with the fuel ( _Cf ) and product ( _Cp) of a components areobtained by replacing the exergy rates ( _ExD). For example, ina turbine, fuel is difference between input and output exergy andproduct is the generated power of the turbine.

In the cost balance formulation (Eq. (20)), there is no cost termdirectly associated with exergy destruction of each component.Accordingly, the cost associated with the exergy destruction ina component or process is a hidden cost. Thus, if one combines theexergy balance and exergoeconomic balance together, one canobtain the following equations:

_ExF;k ¼ _ExP;k þ _ExD;k (23)

where _Exf ;K represents the fuel exergy rate for kth component, and_Exp;K stands for the product exergy rate of kth component, _ExL;K and_ExD;K are the exergy loss and exergy destruction rate of thatcomponent respectively. For example, _ExL;K is the useful energy(exergy) that is wasted to the environment without converting tothe useful form of energy, and _ExD;K is the exergy destruction due tothe irreversibilities. For the turbines, if they are assumed to beadiabatic, _ExL;K is equal to zero. Also, if the pumps are supposed tobe adiabatic, _ExL is equal to zero. Moreover, as for the heaters, ifthey are supposed to operate adiabatically, _ExL;K is equal to zero. Foreach flow line in the system, a parameter that is called flow costrate _C ($/s) is defined.

The last term on the RHS Eq. (29) involves the rate of exergydestruction. As discussed before, if one assumes that the product_Ep;k is fixed and that the unit cost of fuel cF;k of the kth component isindependent of the exergy destruction, one can define the cost ofexergy destruction by the last term of Eq. (20).

26666666666664

_E1 0 0 0 0 0 0 0 0_E1 � _E2 0 0 0 0 _E7 0 00 _E2 � _E3 0 � _E5 � _E6 0 0 00 0 _E3 � _E4 0 0 0 0 _E90 0 0 _E4 � _E5 0 � _E7 � _E8 00 0 0 1 �1 0 0 0 00 0 0 0 0 0 1 �1 00 0 0 0 1 �1 0 0 00 0 0 0 0 0 0 0 1

37777777777775�

26666666666664

c1c2c3c4c5c6c7c8c9

37777777777775

¼

26666666666664

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_CD;k ¼ cF;k _ExD;k (24)

More details of the exergoeconomic analysis, cost balance equa-tions and exergoeconomic factors are completely discussed inreferences [9,10,29].

Thoroughly, several methods have been suggested to expressthe purchase cost of equipment in terms of design parameters in Eq.(20) [22,24e26,30]. However, we have used the cost functionswhich are suggested by Roosen et al. [31]. Nevertheless, somemodifications have been made to tailor these results to the regionalconditions in Iran and taking the inflation rate into account. Forconverting the capital investment into cost per time unit, one maywrite:

_Z-k ¼ Z-k$CRF$4=ðN � 3600Þ (25)

where Zk is the purchase cost of kth component in U.S dollar. Theexpression for each component of the gas turbine plant andeconomic model is presented in Appendix A. N is the annualnumber of the operating hours of the unit, and 4 ¼ 1.06 [21] is themaintenance factor. Finally, in order to determine the cost of exergydestruction of each component, the value of exergy destruction,_ExD;k, is computed using exergy balance equation in the previoussection. The Capital Recovery Factor (CRF) depends on the interestrate as well as estimated equipment life time. CRF is determinedusing the relation [18]:

CRF ¼ ið1þ iÞnð1þ iÞn�1

(26)

Here, i is the interest rate and n is the total operating period of thesystem in years.

4.2. Cost balance equations

To estimate the cost of exergy destruction in each component ofthe plant, we should initially solve the cost balance equations foreach component. Therefore, in application of the cost balanceequation (Eq. (20)), there are usually more than one inlet outletstreams for some components. In this case the numbers ofunknown cost parameters are higher than the number of costbalance equations for that component. Auxiliary exergoeconomicequations are developed to solve this problem [13,21]. Imple-menting Eq. (20) for each component together with the auxiliaryequations forms a system of linear equations as follows:

�_EK�� ½ck� ¼

�_Zk�

(27)

where½ _EK �, ½ck� and ½ _Zk� are the matrix of exergy rate which wereobtained in exergy analysis, exergetic cost vector (to be evaluated)and the vector of ½ _Zk� factors (obtained in economic analysis),respectively.

0� _ZAC� _ZAP� _ZCC� _ZGT000Fc

37777777777775

(28)

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Table 3Constants for Equations (29e32).

Constants 0.3 � 4 � 1.0 1.0 � 4 � 1.6

0.92 � q � 2 2 � q � 3.2 0.92 � q � 2 2 � q � 3.2

A 2361.7644 2315.752 916.8261 1246.1778a 0.1157 �0.0493 0.2885 0.3819b �0.9489 �1.1141 0.1456 0.3479l �1.0976 �1.1807 �3.2771 �2.0365a1 0.0143 0.0106 0.0311 0.0361b1 �0.0553 �0.045 �0.078 �0.085c1 0.0526 0.0482 0.0497 0.0517a2 0.3955 0.5688 0.0254 0.0097b2 �0.4417 �0.55 0.2602 0.502c2 0.141 0.1319 �0.1318 �0.2471a3 0.0052 0.0108 0.0042 0.017b3 �0.1289 �0.1291 �0.1781 �0.1894c3 0.0827 0.0848 0.098 0.1037

P. Ahmadi, I. Dincer / Applied Thermal Engineering xxx (2011) 1e126

Therefore, by solving these sets of equations one can find thecost rate of each line in Fig. 1. Moreover, they are used to find thecost of exergy destruction in each component of the plant.

5. Thermo-enviroeconomic modeling

In order to minimize the environmental impacts, the primarytarget is to increase the efficiency of energy conversion processes,and as a result, decreasing the amount of fuel and the relatedoverall environmental impacts, especially the release of carbondioxide, which is one of the main components of greenhouse gases.Therefore, optimization of thermal systems based on this fact hasbeen an important subject in recent years. Although there are a lotof papers in the literature which are dealing with optimization ofpower plants, generally they do not pay much attention to envi-ronmental impacts. For this reason, one of the major goals of thepresent work is to consider the environmental impacts asproducing the CO and NOx. As it was discussed in [31], the adiabaticflame temperature in the primary zone of the combustion chamberis derived as follow:

Tpz ¼ Asaexp�bðsþ lÞ2

px*qy

*

jz* (29)

where p is dimensionless pressure (P/Pref), q is dimensionlesstemperature (T/Tref), j is the H/C atomic ratio, s ¼ f for f � 1 (f ismass or molar ratio) and s¼ f-0.7 for f� 1. Moreover, x, y and z arequadric functions of s based on the following equations:

x* ¼ a1 þ b1sþ c1s2 (30)

y* ¼ a2 þ b2sþ c2s2 (31)

z* ¼ a3 þ b3sþ c3s2 (32)

In Eqs. (35)e(38), parameters A, a, b, l, ai, bi and ci are constantparameters. More details are presented in [31,32]. All parameters inEq. (36-38) are listed in Table 3.

Table 4The list of constraints for optimization.

Constraints Reason

TIT < 1550 K Material temperature limitP2/P1 < 20 Commercial availabilityhGT < 0.9 Commercial availabilityhAC < 0.9 Commercial availabilityT7 > 400 K To avoid formation of sulfuric acid in exhaust gases

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As it is stated in the literature, the amount of CO and NOxproduced in the combustion chamber and combustion reactionchange mainly by the adiabatic flame temperature. Accordingly,based on reference [32,33] in order to determine the pollutantemission in grams per kilogram of fuel the proper equations areproposed as follow:

mNOx¼ 0:15E16s0:5exp

�� 71100=Tpz�

P0:053 ðDP3=P3Þ0:5(33)

mCO ¼ 0:179E9exp�7800=Tpz

�P23sðDP3=P3Þ0:5

(34)

where s is the residence time in the combustion zone (s is assumedconstant and is equal to 0.002 s); Tpz is the primary zonecombustion temperature; P3 is the combustor inlet pressure;DP3=P3 is the non-dimensional pressure drop in the combustionchamber [33].

6. Multi-objective optimization

6.1. Definition of objective functions, design parameters andconstraints

Two important objective functions including exergy efficiency(must be maximized), the total cost rate of product and environ-mental impact (must be minimized) are considered for multiobjective optimization purpose. The second objective functionexpresses the environmental impact as the total pollution damage($/s) due to CO and NOx emission by multiplying their respectiveflow rates by their corresponding unit damage cost (CCO, CNOx areequal to 0.02086 $/kgCO and 6.853 $/kgNOx) [31,33]. In the presentwork the cost of pollution damage is assumed to be added directlyto the expenditures that must be paid. Therefore, the secondobjective function is sum of the thermodynamic and Environomicobjectives.

The objective function for this analysis is considered as:

� Gas Turbine Power Plant Exergy Efficiency

hTotal ¼_WNet

_mf ;CC � LHV � x(35)

where _WNet, _mf ;CC and x are gas turbine net output power, massflow rate of fuel injected to the combustion chamber andx ¼ 1:033þ 0:0169 y

x � 0:0698x for gaseous fuel with CxHy formula

respectively.

� Total Cost Rate

_CTot ¼ _Cf þXk

_Zk þ _CD þ _Cenv (36)

Table 5Results between the power plant data and simulation code.

Unit Measured Data Simulation Code Difference (%)

T2�C 321.4 332.01 3.19

T6�C 500 529.02 5.48

T7�C 448 487.00 8.01

f_m kg/s 8.44 8.18 3.2

hex % 32.03% 30.41% 5.06

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Fig. 3. The distribution of Pareto optimal points solutions for exergy efficiency andtotal cost rate of the plant.

P. Ahmadi, I. Dincer / Applied Thermal Engineering xxx (2011) 1e12 7

where

_Cenv ¼ CCO _mCO þ CNOX_mNOx

& _CF ¼ cf _mf � LHV (37)

where _Zk, _CF and _CD are purchase cost of each component, fuel costand cost of exergy destruction, respectively. In addition _mCO, _mNOx

are calculated from Eqs. (33) and (34).

6.2. Decision variables

The decision variables (design parameters) in this study arecompressor pressure ratio (rAC), compressor isentropic efficiency(hAC), gas turbine isentropic efficiency (hGT), combustion chamberinlet temperature (T3) and gas turbine inlet temperature (TIT). Eventhough the decision variables may be varied in the optimizationprocedure, each decision variables is normally required to bewithin a reasonable range. The list of these constraints and thereasons of their applications are summarized based on [18,30] andlisted in Table 4.

7. Case study

In order to verify the present simulation code, the results of thisstudy are compared with the actual running gas turbine powerplant in Shahid Salimi Power Plant, Neka, Iran. This power plant islocated near the Mazandaran city near the Caspian Sea, one of thenorthern provinces in Iran. The schematic diagram of this powerplant is shown in Fig. 1. From the power plant data gathered in2005, the incoming air has a temperature of 20 �C and a pressure of1 bar. The pressure increases to10.1 bar through the compressor,which has an isentropic efficiency of 82%. The turbine inlettemperature is 971 �C. The turbine has an isentropic efficiency of86%. The regenerative heat exchanger has an effectiveness of 87%.The pressure drop through the air preheater is considered 3% of theinlet pressure for both flow streams and through the combustionchamber is 3% of the inlet pressure. The fuel (natural gas) is injectedat 20 �C and 30 bar. The results of thermodynamic properties of thecycle form the modeling part and the power plant data are illus-trated in Table 5.

The comparison of simulation code and the actual data from thepower plant shows that the average difference is about 4.98%. Themaximum difference is about 8.01% for air preheater outlettemperature. This verifies the correct performance of developedsimulation code to model this gas turbine power plant.

Fig. 2. Basic concept of Evolutionary algorithm (i.e. Genetic Algorithm).

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8. Results and discussion

8.1. Optimization results

To optimize our system, we have used a genetic algorithmmethod as discussed in reference [33e36] (Fig. 2). The optimizationcode is developed in Matlab software program based on theevolutionary algorithm. Fig. 3 shows the Pareto frontier solution fora gas turbine power plant with the objective functions in the multiobjective optimization section. In this figure, while the total exergyefficiency of the cycle increases to about 42.15%, the total cost rateof products increases only slightly. Increasing the total exergyefficiency from 42.15% to 42.5% is corresponding to the moderateincrease in the cost rate of products. In addition, increase in theexergy efficiency from 42.5% to a higher value leads to a drasticincrease of the total cost rate. Also Fig. 4 shows the exact value ofpoints AeD in Fig. 3. As shown in Fig. 3, the maximum exergyefficiency exists at design point (A) (42.93%), while the total costrate of products is the highest at this point. On the other hand, the

Fig. 4. The distribution of Pareto optimal points solutions for exergy efficiency andtotal cost rate of the plant with their exact value in Fig. 3.

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Table 6Optimum design values for A to D Pareto optimal fronts for input value.

Property Unit A B C D

hex % 42.93 42.78 42.15 41.26_CD;PP $/hr 1463 1453 1428 1418_Cenv $/hr 10.89 10.91 12.28 13.75_CD; Total $/hr 5908 5542 5407 5365

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minimum value for total cost rate of product occurs at design point(D). Design point A is the optimal point at which, efficiency isa single objective function, while design point D is the optimumpoint at which total cost rate of product is a single objective func-tion. The specifications of these sample design points namely AeDin Pareto optimal fronts are listed in Table 6.

It is worth to mention that in multi-objective optimization andthe Pareto solution, each point can be considered as an optimizedpoint. Therefore, selection of the optimum solution depends onpreferences and criteria of each decision-maker. Hence, eachdecision-maker may select a different point as optimum solutionwhich better suits with his/her desires.

8.2. Total cost rate and exergy efficiency

To provide a helpful tool for the optimal design points of the gasturbine cycle in Fig. 3, the following equation is derived for thePareto optimal points curve (Fig. 3).

_CTot ¼ 7:318h3 þ 12:32h2 � 15:15hþ 3:65h4 þ 9:27h3 � 8:65h2 þ 1:89hþ 0:014

� 1000 (38)

By this useful fitted equation, the optimal value of the total costrate of the power plant for each efficiency value can be estimated.

8.3. Comparisons

Table 7 compares the cost rate of product, exergy efficiency, costof environmental impacts of the actual running power plant in Iran(i. e Shahid Salimi Power Plant) and the results from multi-objective optimization. It should be noted that the values formulti-objective is estimated based on point (B) in Fig. 3 because thispoint is the best point in comparisonwith other points in the Paretosolution. This point has the high efficiency and a low total cost ratein comparison with other points. Therefore, all the values here arebased on this point. According to Table 7, the optimization leads tothe 33.56% increment in the total exergy efficiency of the cycle.Moreover, the optimization results show that by using these designparameters one can decrease the total cost of exergy destruction byalmost 36.54%. The important point here is decreasing the cost ofenvironmental impact. Table 7 shows that the difference betweenthe optimized data and the base case lead to decrease the cost of COand NOx by 50.50%.

Table 8 represents the design parameters for both optimizationpoint and case study. As it was mentioned previously, the optimi-zation data is based on point (B) in Fig. 3. In addition, Table 8represents some important exergoeconomic parameters for the gasturbine power plant. From this table, it is understood that

Table 7Comparison between actual power plant parameters and optimized data in thisstudy.

Property Unit Case study Optimized Differences

hex % 32.03 42.78 þ33.56%

Total_C $/hr 7567 5542 �36.54%

env_C $/hr 16.42 10.91 �50.50%

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exergoeconomic factor is an important thermoeconomic parameterthat shows the relative importance of a component cost to theassociated cost of exergy destruction rate in the component.Accordingly, the higher value of exergoeconomic factor implies thatthe major source of the cost for the component under considerationis related to the capital investment and operating and maintenancecosts. The lower value of exergoeconomic factor states that theassociated costs of thermodynamic inefficiencies are much moresignificant than the capital investment and operating and mainte-nance costs for the component under consideration. It can bedetermined from Table 8 that for combustion chamber (CC), therelated cost of exergy destruction is significantly higher than theowning and operating cost of this component and the inefficiencycost for this component is dominant for both base case and opti-mized systems. This is because of the high exergy destruction rate inthe combustion process of the combustion chamber. It is worth tomention that the greatest amount of exergy destruction rate for bothbase case andoptimized case takes place at the combustion chamberbecause of the chemical reaction and the large temperature differ-ence between the burners and the working fluid. In fact, its exergyefficiency is less than other components in the cycle. Further, it canbe found from Table 8 that by applying the optimization, overallexergoeconomic factor of the system increased from32.79 to 62.24%,due to the optimization process causing a decrease in cost of exergydestruction. Table 8 also shows that in all fields, the optimizationprocess improves the total performance of the system in a way thatthe exergy destruction rate is reduced about 23.17%, and the relatedcost of the system inefficiencies decreased about 12.29%.

8.4. Distribution of design parameters

Distribution of optimal design parameters in the Pareto curve isshown in Fig. 5. The lower and upper bounds of these variables aregiven in dotted lines. According to this distribution, it is found thatgas turbine isentropic efficiency and air preheater temperaturereach their maximum values. It shows that increase in these twodesign parameters leads to improvement in both objective func-tions. Therefore, their maximum values are selected. Other designvariables have the scattered distribution. Therefore, it can be pre-dicted that variations of these variables result in conflict betweentwo objective functions in a small range of their variations. To studythis trend and the effects of these design parameters on bothobjective functions at optimal points, the variations of objectivefunction with changes in design parameters for four differentpoints (AeD) in the Pareto curve are shown in next section. Vari-ations of other points have the same trend as these four points.

8.4.1. Sensitivity analyses (Effect of decision variables on objectivefunctions)

Fig. 6-a shows the variation of objective function with changesin compressor isentropic efficiency. It is seen that increase in thisdesign parameter in its allowable range results in increase in gasturbine cycle exergy efficiency, however, this increase leads todecrease in the total cost rate at first, followed by an increase in thetotal cost rate. Therefore, it causes a conflict between objective

Table 8Comparison of design variables between the optimization and case study.

Decision variable Case study Optimization results

rComp 10.10 14.43hComp 0.82 0.86hGT 0.86 0.89TIT(K) 1244.15 1424.8T3(K) 753.56 850

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Fig. 5. Scattering of variables for the Pareto optimal front in Fig.(3).

P. Ahmadi, I. Dincer / Applied Thermal Engineering xxx (2011) 1e12 9

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Fig. 6. Variation of exergy efficiency with total cost rate for five optimum design parameters in four cases of AeD.

P. Ahmadi, I. Dincer / Applied Thermal Engineering xxx (2011) 1e1210

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P. Ahmadi, I. Dincer / Applied Thermal Engineering xxx (2011) 1e12 11

functions. Moreover, since the region where results in improve-ment in both objective functions is greater than a region whichcauses a conflict, this design parameter must have a scattereddistribution near the maximum values. Fig. 5-a confirms this trend.It can be concluded from Fig. 6-b that increase in this parameterleads to increase in exergy efficiency as well as decrease of total costrate. Therefore, higher values of this parameter are favorable fora decision maker.

Fig. 6-c shows the variation of both objective functionswhen gasturbine inlet temperature varies in its allowable range. It is shownthat increase in this design parameter leads to increase in theexergy efficiency, however, it results in decrease of the total costrate first and then this increase causes a drastic increment in totalcost rate of the plant. It can be explained that an increase in TIT aftera reasonable range results in increase of the cost of a combustionchamber which directly affects the total cost rate of the plant.

The effects of increasing the compressor pressure ratio on bothobjective functions are shown in Fig. 6-d. Increase in compressorpressure ratio leads to increase in gas turbine exergy efficiency forall ranges, but it decreases the total cost rate first and then itincreases the total cost rate of the plant. This trend is like thevariations of TIT on total cost rate in Fig. 6-c.

As it is shown in Fig. 6-e, the increase in the air preheatertemperature (T3) leads to improvement on both objective functions.This is why the optimal points in Fig. 5-e reach their higher values.Therefore, variations of this parameter do not cause a conflictbetween two objective functions.

9. Conclusions

In the present study, thermodynamic and exergoeconomicmodeling of a gas turbine power plant with optimization wascarried out. To achieve this aim, a simulation code was developed inMatlab software program. In order to validate the simulation code,the results were compared with the actual data obtained fromactual running gas turbine power plant in Iran. The results showeda reasonably well agreement between simulation code and exper-imental data. Moreover, a multi objective genetic algorithm wasused to optimize the two important objective functions. The firstobjective functionwas the cycle exergy efficiency and the other oneswere total cost rate of the plant including investment cost, cost ofexergy destruction and cost of environmental taxes. In addition, theresults of optimization data were compared with the actual datafrom the power plant. Their results showed that by selecting thesesets of design parameters 33.56% increment in the total exergyefficiency is achieved while this values from multi objective opti-mization leads to decrease the environmental impacts of the plantfor about 50.50%, which has significant importance. Finally,a sensitivity analysis of the variation of each design parameter onboth objective functions was carried out and discussed in detail. Insummary, we can extract some concluding remarks:

� Increasing the compressor isentropic efficiency leads to anincrease in the total exergy efficiency of the cyclewhile increasingthis parameter decreases the total cost at first, followed by anincrease.

� Increase in the gas turbine isentropic efficiency results inimprovement in both objective functions. It means that thisparameter does not lead to a conflict between objectivefunctions.

� Increase inTIT leads to increase in the exergy efficiency, however,it results in decrease of the total cost rate first and then thisincrease causes a drastic increment in total cost rate of the plant.

� The effect of increase in the air preheater temperature leads toimprovement in both objective functions, thus the maximum

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values of this design parameters are selected in the optimiza-tion procedure.

Appendix. Nomenclature

C Cost per unit of exergy ($/Mj)Cp Specific heat (kJ/kg K)_CD Cost of exergy destruction ($/h)Cf Cost of fuel pet unit of energy ($/Mj)Ex Exergy (kJ)e Specific exergy (kJ/kg)h specific enthalpy (kJ/kg)_ExD Exergy Destruction (kJ)LHV Lower Heating Value (kJ/kg)_m Mass Flow rate (kg/s)P Pressure (bar)Q Heat Transfer (kJ)R Gas constant (kJ/kg. �K)s specific entropy (kJ/kg K)T Temperature (

�C)

TPZ Adiabatic temperature in the primary zone of combustionchamber (

�K)

W Work (kJ)x Molar Fraction_Z- Capital cost rate ($/s)Zk purchase cost of the component ($)

Greek symbolsh EfficiencyhGT Gas Turbine isentropic efficiencyhAC Air Compressor isentropic efficiencye CO2 emission per net output power (kgCO2/MWhr)g Specific heat ratio4 maintenance factorx Coefficient of Fuel Chemical exergy

Subscripts and superscriptsa Airamb AmbientAP Air PreheaterAC Air CompressorCC Combustion ChamberCh ChemicalCRF Capital Recovery FactorD Destructione Exit Conditionenv EnvironmentGT Gas Turbinef Fuelg Combustion gassesh Houri Interest ratein Inlet Conditionk ComponentL LossOpt Optimumph PhysicalPP Power PlantRAC Compressor pressure ratioref Referencetot Total+ Reference ambient condition$ Rate

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